A model of quantum computation is specified by its state space, an
initial state and a generating set of quantum operations for manipulating
states. At least one of these operations should involve a classical output for
readout. There are now a number of models where the quantum operations are
associated with discrete or continuous groups. So far, these models are either
efficiently classically simultable in a strong sense, or they can realize
standard quantum computers faithfully. An interesting case study involves
linear optics for fermions or bosons with particle detectors. The former is
computationally weak, while the second can be used to realize quantum
computers.
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